Statistical foundations · estimates and uncertainty

Read the estimate and its confidence interval.

Use the point estimate to describe what was observed and the interval to judge precision, plausible magnitude and what remains uncertain.

Use this when: an output gives you an estimate and a 95% confidence interval.
You will learn: how large the observed effect is, how precise it is and what remains uncertain.
Then choose: the plain-language p-value guide or return to your analysis.

The central idea

A p-value cannot tell you how large a medical difference is.

First read what was estimated, in what units and in which direction. Then use the interval to see the range of values still reasonably compatible with the data and model.

Helpful first: use the statistical-foundations guide if samples and target populations are new to you.

By the end you can

distinguish a population quantity from a sample estimate;
explain what a standard error represents;
interpret a 95% confidence interval without claiming a 95% probability;
identify the null value for a difference and a ratio;
separate statistical precision from clinical importance and bias.

1 · Estimate and uncertainty

Move from the target quantity to the observed range.

Population quantity

What you want to know

For example, the reviewed-versus-unreviewed six-month disability prevalence difference in the target population.

Point estimate

What this sample observed

One best estimate calculated from the available participants, such as a 0.6 percentage-point difference.

Standard error

How estimates vary under repeated sampling

It reflects sample size, variability and design under the chosen statistical model.

95% confidence interval

A procedure with long-run coverage

Across repeated comparable studies, 95% of intervals made this way would contain the true parameter if the assumptions held.

Do not say there is a 95% probability that this already calculated frequentist interval contains the true value. The interval’s reliability is conditional on the design, model and assumptions and does not measure bias.

2 · Description

Even a percentage is an estimate.

Example · six-month disability prevalence

Among reviewed participants with observed disability, 45 of 200 had disability: 22.5%. The numerator, denominator, outcome definition and six-month time point are part of the estimate. A confidence interval would describe sampling precision; it would not repair missing outcomes or make the cohort representative of every older adult.

3 · Group comparisons

Read effect, interval and clinical context before the test.

Welch comparison · quality of life

Mean difference −0.001; 95% CI −0.020 to 0.018.

Direction and size: The observed reviewed-minus-unreviewed mean difference is almost zero.
Compatible range: The data and model remain compatible with a decrease of 0.020 through to an increase of 0.018 points.
Null value: Zero is inside the interval, but this does not prove equal means.
Clinical meaning: Compare the full interval with a justified clinically important difference, not only zero.

Disability prevalence comparison

Difference +0.6 percentage points; 95% CI −6.2 to +7.4.

Point estimate: Observed six-month disability prevalence is slightly higher in the reviewed group.
Precision: The interval is wide enough to include clinically relevant differences in either direction.
Conclusion: Do not replace that uncertainty with “the groups were the same” merely because p>0.05.

4 · Differences and ratios

Know which null value belongs to the effect scale.

Effect scale	Null value	Shared-cohort reading
Mean or proportion difference	0	No absolute difference between groups.
Proportion, risk, odds, rate or hazard ratio	1	The numerator group has the same relative quantity as the reference group.

Example · proportion ratio 1.03; 95% CI 0.76 to 1.40

The point estimate suggests six-month disability prevalence was 1.03 times as high with review. The interval is compatible with prevalence 24% lower through to 40% higher. It includes 1 and is too wide to establish equivalence.

5 · Regression

Keep adjustment, scale and uncertainty together.

Example · adjusted disability odds ratio 0.64; 95% CI 0.41 to 1.01

After the pre-specified adjustment, the reviewed group had an estimated 36% lower odds of disability. The interval is compatible with substantially lower odds through to almost no difference. It is conditional on the model, covariates, functional forms, analysis population and assumptions. Odds are not risks, and adjustment does not automatically create a causal effect.

Methods

Name the outcome, model, reference group, covariates, analysis population and how the interval was calculated.

Results

Report the estimate and 95% CI with units or effect scale, then the p-value if it serves a planned test.

Discussion

Compare the compatible range with clinical importance and explain bias, confounding and assumption limits.

6 · A fixed reading order

Use the same six questions every time.

01
What quantity and units?
Prevalence, mean difference, odds ratio, rate ratio or another named estimand.
02
Which direction and reference?
State numerator, comparator and coding.
03
How large is the point estimate?
Translate it into medically intelligible language.
04
How wide is the interval?
State the range of effects compatible with the data and model.
05
Where are the null and clinical threshold?
They answer different questions.
06
Which assumptions and biases remain?
Precision is not validity and association is not automatically causation.

Reading this result in a paper? Use the paper-appraisal guide to keep the estimate with the study design, denominators, bias and relevance.

7 · Beginner self-check

Choose the defensible interpretation.

“The 95% CI includes 1, so there is no association.” Correct?

No. State the point estimate and the full compatible range. Inclusion of the null is not proof of no association or equivalence.

Would doubling the sample automatically remove confounding?

No. More information may narrow the interval around the same biased estimate. Design, measurement and causal adjustment determine validity.

Can a narrow interval still be clinically unhelpful?

Yes. A precise estimate may concern a trivial effect, the wrong target population or a biased comparison. Precision is only one part of interpretation.

ContinueUnderstand where a p-value comes from →Follow the data through a test statistic and null reference distribution to the reported probability.

Go deeper · confidence intervals in medical research

Optional authoritative sources for interval estimation, interpretation and reporting.

Clinical statistics · BMJ